For a many-to-one matching market where firms have strict and $\mathit{q}$-responsive preferences, we give a characterization of the set of strongly stable fractional matchings as the union of the convex hull of all connected sets of stable matchings. We also prove that a strongly stable fractional matching is represented by a lottery of stable matchings that are ordered in the common preferences of all firms.

中文翻译：

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关于多对一强稳定分数匹配的集合

对于多对一的匹配市场，企业必须严格遵守 $\mathit{q}$-响应偏好，我们将一组高度稳定的分数匹配的特征描述为所有稳定匹配的连接集的凸包的并集。我们还证明了，一个非常稳定的分数匹配由一系列稳定匹配的彩票表示，这些彩票按所有公司的共同偏好排序。